Lemma 2.9 [1]}
Suppose \(x \ge y >\log x\)  and let \(u=\log x/ \log y\) . We have, in the notation of Lemma REF ,
\( (1-\alpha )\log y = \xi (u) + O\left(\frac{1}{u}+\frac{\log x}{y}+e^{-\sqrt{\log y}}\right).\) 

